3/4y-6=1/4y*10

Solution for 3/4y-6=1/4y*10 equation:

3/4y-6=1/4y*10

We move all terms to the left:

3/4y-6-(1/4y*10)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 4y*10)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(+1/4y*10)-6=0

We get rid of parentheses

3/4y-1/4y*10-6=0

We calculate fractions


120y/160y^2+(-4y)/160y^2-6=0

We multiply all the terms by the denominator


120y+(-4y)-6*160y^2=0

Wy multiply elements

-960y^2+120y+(-4y)=0

We get rid of parentheses

-960y^2+120y-4y=0

We add all the numbers together, and all the variables

-960y^2+116y=0

a = -960; b = 116; c = 0;
Δ = b2-4ac
Δ = 1162-4·(-960)·0
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-116}{2*-960}=\frac{-232}{-1920}
=29/240
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+116}{2*-960}=\frac{0}{-1920}
=0
$